Finite Group Databasebeta

← D₁₃×C₂₉×C₄₃ #44569788

Subgroups — D₁₃×C₂₉×C₄₃ #44569788

Order 32422.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₂₉×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₂₉×C₄₃	—	13	1	no	maximal, Hall
3	C₂₉×C₄₃	D₁₃	1	1	yes	characteristic, direct product factor, Hall
4	D₁₃×C₄₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₁₃×C₂₉	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₄₃	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
7	C₁₃×C₂₉	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₄₃	—	13	1	no	Hall
9	C₂×C₂₉	—	13	1	no	Hall
10	C₄₃	D₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
11	C₂₉	D₁₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
12	D₁₃	C₂₉×C₄₃	1	1	yes	characteristic, direct product factor, Hall
13	C₁₃	C₂×C₂₉×C₄₃	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉×C₄₃	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₂₉×C₄₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₂₉×C₄₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂₉×C₄₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×C₂₉×C₄₃	C₂	semidirect
3. C₂₉×C₄₃	D₁₃	direct (N × H)
4. D₁₃×C₄₃	C₂₉	direct (N × H)
5. D₁₃×C₂₉	C₄₃	direct (N × H)
6. C₁₃×C₄₃	C₂×C₂₉	semidirect
7. C₁₃×C₂₉	C₂×C₄₃	semidirect
10. C₄₃	D₁₃×C₂₉	direct (N × H)
11. C₂₉	D₁₃×C₄₃	direct (N × H)
12. D₁₃	C₂₉×C₄₃	direct (N × H)
13. C₁₃	C₂×C₂₉×C₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×C₂₉×C₄₃	2
C₂×C₂₉×C₄₃	13
D₁₃×C₄₃	29
D₁₃×C₂₉	43